Stock market participation and IQ.Refer to The Journal of Finance(December 2011) study of whether the decisionto invest in the stock market is dependent on IQ, Exercise3.46 (p. 182). The summary table giving the number ofthe 158,044 Finnish citizens in each IQ score/investment category is reproduced below. Again, suppose one of the citizens is selected at random.

IQ Score	Invest in Market	No Investment	Totals
1 2 3 4 5 6 7 8 9	893 1,340 2,009 5,358 8,484 10,270 6,698 5,135 4,464	4,659 9,409 9,993 19,682 24,640 21,673 11,260 7,010 5,067	5,552 10,749 12,002 25,040 33,124 31,943 17,958 12,145 9,531
Totals	44,651	113,393	158,044

Source:Based on M. Grinblatt, M. Keloharju, and J. Linnainaa, “IQ and Stock Market Participation,” The Journal of Finance, Vol. 66, No. 6, December 2011 (data from Table 1 and Figure 1).

a.Given that the Finnish citizen has an IQ score of 6 or higher, what is the probability that he/she invests in the stock market?

b.Given that the Finnish citizen has an IQ score of 5 or lower, what is the probability that he/she invests in the stock market?

c.Based on the results, parts a and b, does it appear that investing in the stock market is dependent on IQ? Explain.

As we only want the probability for citizens with IQ scores of 6 and above, we will first add the number of citizens in all 3 columns with an IQ of 6 and above.

Invest in Market = 10,270+ 6698 + 5135 + 4464 = 26,567

No investment = 21673 + 11260 + 7010 + 5067 = 45,010

Total = 26567 + 45010 = 71,577

Let A be the total number of people with an IQ of 6 or above.

B be the number of people with an IQ of 6 or above who invest in the market.

To find the probability that the Finnish citizen has an IQ score of 6 or higher and invests in the stock market,

$\begin{array}{c}\text{P=}\frac{\text{B}}{\text{A}}\\ \text{=}\frac{\text{26567}}{\text{71577}}\\ \text{=0.37}\\ \text{=37\%}\end{array}$

Therefore,$P\left(B|A\right)=37\%$.

Let’s add the number of citizens with an IQ of 5 or less for all columns,

Invest in Market = 893 + 1340 + 2009 + 5358 + 8484 = 18,084

No investment = 4659 + 9409 + 9993 + 19682 + 24640 = 68,383

Total = 18084 + 68383 = 86,467

Let’s assume

C = total number of people with an IQ of 5 or below

D = number of people with an IQ of 5 or below who invest in the market

$\begin{array}{c}\text{P=}\frac{\text{D}}{\text{C}}\\ \text{=}\frac{\text{18084}}{\text{86467}}\\ \text{=0.2091}\\ \text{=20.91\%}\end{array}$

Therefore,$P\left(C|D\right)=20.91\%$

$\text{P}\left(\text{B|A}\right)\text{>P}\left(\text{C|D}\right)$

Investing in stocks does depend on IQbecause the probability that a citizen with IQ of 6 or above is greater than the probability of a citizen investing who has IQ of 5 or below.

There are more chances that a person with a higher than 6 IQ will invest in stocks.